I bought a Pi to support my ham radio hobby. I figured I could do digital modes like PSK-31 or RTTY with it, and if I accidentally sent 100 watts of RF into it, I'd kill a $35 circuit board rather than my $2,000 laptop. It hasn't seen that use yet. It got used as baby's first linux box, and I've done some I/O projects with it.
Then I bought an Arduino to have analog in ability, and I use it more than the Pi now. I'll work on some demonstrations of some of my projects, but here are some of the highlights:
Pain-O-Mat: Displays "Squeeze me" on a dot matrix display, and when you squeeze the pressure sensitive resistor hard enough, the message changes to "OW!"
Therm-O-Morse: Press a button, and it blinks and beeps the current temperature in Morse code using my own Morse code library.
My crowning achievement was Etch. It uses an Arduino and a computer (the Pi works just fine) to simulate an Etch-A-Sketch. It was quite a challenge to get two programs running on different hardware written in different languages at different speeds to work together.